This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195265 #57 Oct 09 2017 15:31:06
%S A195265 20,225,3252,223271,297699,399233,715623,3263907,32347303,160720129,
%T A195265 1153139393,72171972859,736728093411,3245576031137,11295052366467,
%U A195265 310807934835791,1789205424940407,31745337977379983,1122916740775279751,7251536377635958081,151243563319717018007
%N A195265 Trajectory of 20 under iteration of the map x -> A080670(x).
%C A195265 The table that I submitted for A195264 (see the second link here) is still actively maintained by me. That includes all unknown-outcome evolutions starting with numbers up to 10000. If you click in that table on the 'unknown' beside the number 20 it will give you the current state of the evolution of the number 20. There was a bottleneck at Alonso20(102) [= A195265(103); we're using offset zero for our evolutions] involving a 62-digit factor, cracked by "Mathew" in MersenneForum on August 13. _Sean A. Irvine_ subsequently extended that to Alonso20(109). The unfactored composite in Alonso20(110) is 178 digits long. I maintain links to sorted lists of unfactored composites at the bottom of the table. If anyone can factor any of these composites, submit the factorization to factordb.com and I will (eventually) find it; a personal heads-up would of course be appreciated. - _Hans Havermann_, Oct 27 2013
%H A195265 Hans Havermann, <a href="/A195265/b195265.txt">Table of n, a(n) for n = 1..110</a>
%H A195265 Hans Havermann, <a href="http://chesswanks.com/seq/a195264/">Table of n, A195264(n) for n = 1..10000</a> (includes links to lengthy (>40) and unknown-outcome evolutions, and a list of unfactored composites in the unknowns' last step)
%H A195265 N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, <a href="https://vimeo.com/237029685">Part I</a>, <a href="https://vimeo.com/237030304">Part 2</a>, <a href="https://oeis.org/A290447/a290447_slides.pdf">Slides.</a> (Mentions this sequence)
%e A195265 20 = 2^2*5 -> 225 = 3^2*5^2 -> 3252 = 2^2*3*271 -> 223271 ...
%p A195265 # See A195266
%t A195265 A080670[n_] := ToExpression@StringJoin[ToString/@Flatten[DeleteCases[FactorInteger[n], 1, -1]]]; NestWhileList[A080670, i = 1; 20, (PrintTemporary[{i++, #}]; ! PrimeQ[#]) &, 1, 40] (* _Wouter Meeussen_, Oct 27 2013 *)
%Y A195265 Cf. A037274, A080670, A195264, A195266, A230305.
%K A195265 nonn,base
%O A195265 1,1
%A A195265 _N. J. A. Sloane_, Sep 14 2011, based on a posting to the Sequence Fans Mailing List by _Alonso del Arte_
%E A195265 _Alonso del Arte_ computed 40 terms, _D. S. McNeil_ extended it to 66 terms, _Sean A. Irvine_ to 70 terms, _Hans Havermann_ (Oct 27 2013) to 110 terms.